Reduced-Time Migration of Converted Waves David Sheley and Gerard T. Schuster University of Utah.

Reduced-Time Reduced-Time Migration of Migration of

Converted WavesConverted Waves

David Sheley and Gerard T. David Sheley and Gerard T. SchusterSchuster

University of UtahUniversity of Utah

OutlineOutline• MotivationMotivation• Reduced-Time Migration TheoryReduced-Time Migration Theory• Error AnalysisError Analysis• ResultsResults

– Synthetic DataSynthetic Data– Field DataField Data

• ConclusionsConclusions

Problem: Dark FlanksProblem: Dark FlanksD

epth

Dep

th

OffsetOffset

00

ZZ

Rec

eive

r W

ell

Sou

rce

Wel

l

XX00

?? ??

PPPP

?? ???? ??

m(r) = d(zm(r) = d(zgg, , sr sr ++ rgrg))

PP

Solution: PS Transmission MigrationSolution: PS Transmission MigrationD

epth

Dep

th

OffsetOffset

00

ZZ

Rec

eive

r W

ell

Sou

rce

Wel

l

XX00

PSPSPP

PSPS

m(r) = d(zm(r) = d(zgg, , sr sr ++ rgrg))

MotivationMotivation

• Solutions:Solutions:1.1. PS Transmission MigrationPS Transmission Migration

• Problems:Problems:1.1. Dark FlanksDark Flanks


• Solutions:Solutions:1. PS Transmission Migration

• Problems:Problems:1. Dark Flanks

2.2. Velocity Errors (Vp, Vs)Velocity Errors (Vp, Vs)


• Solutions:Solutions:1. PS Transmission Migration2.2. Reduced-Time MigrationReduced-Time Migration

• Problems:Problems:1. Dark Flanks

2.2. Velocity Errors (Vp, Vs)Velocity Errors (Vp, Vs)

Reduced-Time MigrationReduced-Time Migration1. Data time shift1. Data time shift

Dep

th (

m)

Dep

th (

m)

Time (ms)Time (ms)PP

PSPS

SS

d(zd(zgg, t , t

d(zd(zgg, t , t


Time (ms)Time (ms)

PPPSPS

SS

Dep

th (

m)

Dep

th (

m)

obsobsd’(g, t) = d(zd’(g, t) = d(zgg, t + , t + sg sg


d’(zd’(zgg, t) = d(z, t) = d(zgg, t , t

sgsgObserved direct-P traveltimeObserved direct-P traveltimeobsobs

2. Modify the migration equation2. Modify the migration equation

m(r) = d’(zm(r) = d’(zgg, , sr sr ++ rg rg ))

obsobssgsg

calccalc–– sgsg

Focusing-Time ErrorFocusing-Time ErrorConventional vs. Reduced-TimeConventional vs. Reduced-Time

Reduced-TimeReduced-Time (d(dsr sr ++ ddrg rg psr psr --

ddsg)sg)c/cc/c

ConventionalConventional (d(dsr sr ++ ddrg rg psrpsr))c/cc/c22

22

00

0000

00250250

250250

500500

500500

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)

Dep

th (

m)

Dep

th (

m)


00

1212

88

44

1616

Focusing-Time ErrorFocusing-Time Error

ImagingImaging ErrorError (ms)(ms)

ConventionalConventionalTrans. PSTrans. PSMigrationMigration

Reduced-Reduced-TimeTimeMigrationMigration

Crosswell ModelCrosswell Model

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m) 11411400114114

00

VVpp /V /Vss = 1.5 = 1.5

Well Separation Well Separation = 100 m= 100 m

Source = 1500 HzSource = 1500 Hzds = 2 mds = 2 mdg = 2 mdg = 2 m

5000 m/s5000 m/s

5500 m/s5500 m/s

Synthetic DataSynthetic DataD

epth

(m

)D

epth

(m

)

00

1141142020 3535Time (ms)Time (ms)

Original DataOriginal Data

Dep

th (

m)

Dep

th (

m)

00

1141148822 Time (ms)Time (ms)

Shifted Muted DataShifted Muted Data

SPSPPSPS

PP

PSPS SS

SPSP

Conventional PS Conventional PS Transmission Migration Transmission Migration

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)00114114

00

100100

True VelocityTrue Velocity

Conventional PS Conventional PS Transmission Migration Transmission Migration

Dep

th (

m)

Dep

th (

m)


00

100100

True VelocityTrue Velocity + 10 % Velocity+ 10 % Velocity

Offset (m)Offset (m)00 100100

Dep

th (

m)

Dep

th (

m)


00

100100


Reduced-Time PS MigrationReduced-Time PS Migration

Dep

th (

m)

Dep

th (

m)


00

100100


Reduced-Time PS MigrationReduced-Time PS Migration

+ 10 % Velocity+ 10 % Velocity


Dep

th (

m)

Dep

th (

m)


00

100100

Conventional PSConventional PS

Comparison +10% VelocityComparison +10% Velocity

Recuced-TimeRecuced-Time


km/s

eckm

/sec6.06.0

5.05.0

7.07.0

Kidd Creek CrosswellKidd Creek Crosswell

WellWell

00

2020

4040

6060

505000

ReceiverReceiverWellWell

SourceSource

Dep

th (

m)

Dep

th (

m)


• Time Delay = 3 ms ?Time Delay = 3 ms ?

• Well LocationWell Location

• Velocity ModelVelocity Model

Data ProblemsData Problems

66Time (ms)Time (ms)

00

2020

4040

6060

Dep

th (

m)

Dep

th (

m)

00

Time Shifted CRGTime Shifted CRG

ConventionalConventional00

2020

6060

505000 Offset (m)Offset (m)

Dep

th (

m)

Dep

th (

m)

ConventionalConventional00

2020

6060

505000 Offset (m)Offset (m) Offset (m)Offset (m) 505000

Reduced-TimeReduced-TimeD

epth

(m

)D

epth

(m

)

ConclusionsConclusions• Transmission PS migration can image Transmission PS migration can image

structure invisible to reflection migration.structure invisible to reflection migration.

• Reduced-time migration decreases the Reduced-time migration decreases the migration error of an incorrect velocity migration error of an incorrect velocity model.model.

• PS reduced-time migration can successfully PS reduced-time migration can successfully image a transmitting boundary.image a transmitting boundary.

AcknowledgementsAcknowledgements

I sincerely thank the 1999 sponsors I sincerely thank the 1999 sponsors of the UTAM consortium for their of the UTAM consortium for their financial support.financial support.

Reduced-Time Migration of Converted Waves David Sheley and Gerard T. Schuster University of Utah.

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Transcript of Reduced-Time Migration of Converted Waves David Sheley and Gerard T. Schuster University of Utah.